They are not native to the Disc, but come from a "parasite universe", sometimes called Fairyland. This pocket dimension can latch onto different universes at certain times, allowing the elves (and other fae creatures such as unicorns, Jenny Greenteeth and, before they were cast out, the Nac Mac Feegle) to go hunting.
One of the things they hunt is people. Elves have no proper imagination or real emotions, and therefore such things fascinate them. Because they cannot create they steal musicians and artists. Because they cannot have children (although they are capable of breeding with humans, resulting in offspring with superficially elvish characteristics - skinny, pointy ears, a tendency to giggle and burn easily in the sun - but fundamentally human traits i.e. empathy) they steal children from the Disc to be their toys. Because they cannot feel empathy they enjoy the suffering of others. Even if an elf is, for reasons of its own, trying to be nice, its lack of understanding of humans mean there's always something "off" about it.
Mostly they get away with this, due to the illusion-creating glamour they cast. While elves are, as mentioned above, not musical, elfsong is perceived as beautiful by humans, and is highly hypnotic. Elves are generally seen as innately beautiful and stylish, but this is just another aspect of the glamour. Some of them are only vaguely humanoid.
The glamour does not seem to have as much effect on trolls and dwarfs, partly because they lack the romantic imagination to let it work and partly because of their connection to iron. Elves can be seen as the direct opposite of Prattchet's other recurring villains the auditors of reality as, while both have intentions hostile to life, elves lead chaotic existences unfettered by laws, rules and restrictions, as opposed to the totally ordered auditors. Elves, in fact, don't even seem to have a concept of rules.
Elves have copper-based, blue-green blood, and are extremely vulnerable to iron. This is partly because there is no way of magicking iron, and partly that they have the ability to detect magnetic fields, and use them to navigate (as pigeons are thought to do) and even sense the thoughts of others from short distances. The presence of iron disrupts this and sends them into a panic. The main gateway to the world of Elves in Lancre is surrounded by several large boulders of naturally magnetised meteoric iron. When there is no iron around they have the absolute confidence of beings who know exactly where they are.
Rational thought and the absence of superstition, which makes the glamour harder, is referred to by Nanny Ogg as "iron in the head".
Elves are ruled by a King and Queen. They act much the same as the King and Queen in chess, the Queen is the most obvious ruler, organising the raiding parties and maintaining absolute control of her kingdom. The King (who bears some similarity to Cernunnos or Herne) tends not to get involved if he can avoid it and keeps to himself in a different aspect of Fairyland (possibly the Discworld version of Annwn). The King and Queen may once have ruled together, but it has been implied there was an acrimonious split, which brings to mind the rift between the fairy courts of Oberon and Titania in A Midsummer Night's Dream.
If it comes to that, there may not only be one King and Queen. However, due to the elves' lack of imagination and creativity any Kings and Queens of the Elves tend to be similar.